Analysis of Linear Systems with Input Saturation and Model Uncertainty: An LMI Approach

The analysis of uncertain linear time invariant (LTI) systems with input saturation has been addressed here in a linear matrix inequality (LMI) framework. The polytopic and norm bounded model uncertainties are considered. The LMI approach gives less conservative results and is computationally attractive. The circle and Popov criteria have been applied to analyze the stability and performance of the system in a convex optimization framework. For stability, a local analysis has been performed leading to maximization of the region of attraction of the system and for performance, the disturbance rejection problem has been taken up into the analytical framework. The optimization problem posed in LMI framework has been solved using MATLAB LMI toolbox and two numerical examples have been illustrated to show the efficacy of the proposed methods.